Question

A poll found that 68.3​% of citizens felt the government was not working well. If seven people were randomly​ selected, what is the probability that all seven felt the government is not working​ well?

Answer 1

The probability that all seven randomly selected people feel that the government is not working well is approximately 0.107 or 10.7%.

Step-by-step explanation:

To find the probability that all seven people randomly selected felt that the government was not working well, we can use the concept of independent events. The probability of one person feeling that the government is not working well is 68.3% or 0.683. Since the events are independent, we can multiply the probabilities together for all seven people:

P(all seven feel the government is not working well) = 0.683 * 0.683 * 0.683 * 0.683 * 0.683 * 0.683 * 0.683 ≈ 0.107

Therefore, the probability that all seven randomly selected people feel that the government is not working well is approximately 0.107 or 10.7%.

Answer 2

Answer: 0.0693

Step-by-step explanation:

Given : The probability of citizens felt the government was not working well = 0.683

The binomial distribution formula :-

`^nC_x\ p^x\ (1-p)^(n-x)`, where n is the number of trials and p is the probability of successes.

If seven people were randomly​ selected, then the probability that all seven felt the government is not working​ well is given by :-

`P(x=7)=^7C_7\ (0.683)^7\ (1-0.683)^(7-7)\\\\=(1) (0.683)^7\(1)=0.0693337876116\approx0.0693`

Thus , the required probability : 0.0693